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Simplifying 0 = (4x + 12)(x)(0.25x + 2) Reorder the terms: 0 = (12 + 4x)(x)(0.25x + 2) Reorder the terms: 0 = (12 + 4x) * x(2 + 0.25x) Reorder the terms for easier multiplication: 0 = x(12 + 4x)(2 + 0.25x) Multiply (12 + 4x) * (2 + 0.25x) 0 = x(12(2 + 0.25x) + 4x * (2 + 0.25x)) 0 = x((2 * 12 + 0.25x * 12) + 4x * (2 + 0.25x)) 0 = x((24 + 3x) + 4x * (2 + 0.25x)) 0 = x(24 + 3x + (2 * 4x + 0.25x * 4x)) 0 = x(24 + 3x + (8x + 1x2)) Combine like terms: 3x + 8x = 11x 0 = x(24 + 11x + 1x2) 0 = (24 * x + 11x * x + 1x2 * x) 0 = (24x + 11x2 + 1x3) Solving 0 = 24x + 11x2 + 1x3 Solving for variable 'x'. Remove the zero: -24x + -11x2 + -1x3 = 24x + 11x2 + 1x3 + -24x + -11x2 + -1x3 Reorder the terms: -24x + -11x2 + -1x3 = 24x + -24x + 11x2 + -11x2 + 1x3 + -1x3 Combine like terms: 24x + -24x = 0 -24x + -11x2 + -1x3 = 0 + 11x2 + -11x2 + 1x3 + -1x3 -24x + -11x2 + -1x3 = 11x2 + -11x2 + 1x3 + -1x3 Combine like terms: 11x2 + -11x2 = 0 -24x + -11x2 + -1x3 = 0 + 1x3 + -1x3 -24x + -11x2 + -1x3 = 1x3 + -1x3 Combine like terms: 1x3 + -1x3 = 0 -24x + -11x2 + -1x3 = 0 Factor out the Greatest Common Factor (GCF), '-1x'. -1x(24 + 11x + x2) = 0 Factor a trinomial. -1x((8 + x)(3 + x)) = 0 Ignore the factor -1.Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(8 + x)' equal to zero and attempt to solve: Simplifying 8 + x = 0 Solving 8 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + x = 0 + -8 x = 0 + -8 Combine like terms: 0 + -8 = -8 x = -8 Simplifying x = -8Subproblem 3
Set the factor '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Simplifying x = -3Solution
x = {0, -8, -3}
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